Field flattener lens

Not to be confused with Flat-field correction, which improves brightness uniformity.

Field flattener lens is a type of lens used in modern binocular designs^[a] and in astronomic telescopes to improve edge sharpness. Field flattener lenses counteract the Petzval field curvature of an optical system, mitigating the field-angle dependence of the focal length of a system.

Details

The object in designing a field flattening lens is to create a lens that shifts the focal points of the Petzval surface to lie in the same plane. Consider inserting a pane of glass in a focusing beam. Due to refraction, the focal point of the beam is shifted by ${\displaystyle \delta _{x}}$ dependent on the thickness of the glass. Thus we have a thickness as a function of focal shift:

${\displaystyle t(\delta _{x})=\left({\frac {n}{n-1}}\right)\delta _{x}}$.

${\displaystyle \delta _{x}(y)}$ is given by the radius of curvature of the Petzval surface, ${\displaystyle R_{p}}$. It can be shown, then, that the radius of curvature for the lens that would flatten out the field is given by

${\displaystyle R_{f}=\left({\frac {n-1}{n}}\right)R_{p}.}$ ^[1]

Examples of use

In the 21st century, the New Horizons spacecraft, which was an unmanned space probe sent past Pluto and the Kuiper belt, had a telescope instrument called the Long Range Reconnaissance Imager.^[2] LORRI was a reflecting telescope but incorporated a field-flattening lens, with three elements.^[2]

See also

• Petzval field curvature
• Coma corrector

Notes

1. E.g. Canon 10 x 42 L IS WP, 18 x 50 IS All Weather and Swarovski EL 8.5 x 42, EL 10 x 42.